What Are Degrees of Belief?

Probabilism is committed to two theses: 1) Opinion comes in degrees—call them degrees of belief, or credences. 2) The degrees of belief of a rational agent obey the probability calculus. Correspondingly, a natural way to argue for probabilism is: i) to give an account of what degrees of belief are, and then ii) to show that those things should be probabilities, on pain of irrationality. Most of the action in the literature concerns stage ii). Assuming that stage i) has been adequately discharged, various authors move on to stage ii) with varied and ingenious arguments. But an unsatisfactory response at stage i) clearly undermines any gains that might be accrued at stage ii) as far as probabilism is concerned: if those things are not degrees of belief, then it is irrelevant to probabilism whether they should be probabilities or not. We would like to take a step back and scrutinize the state of play regarding stage i). Indeed, we find it surprising that it hasn't been given more scrutiny than it has. Surprising, because 'degree of belief' is the central notion in subjective probability theory, the core concept around which the entire theory is built. 'Degree of belief' is supposed to underwrite a more plausible and nuanced probabilist epistemology than the traditional 'Cartesian' epistemology that traffics only in binary, all-or-nothing notions such as 'knowledge' and 'belief'. Meanwhile, 'degree of belief' is also offered as an interpretation of the probability calculus, sitting proudly alongside the classical, frequentist, logical, and propensity interpretations. Thus, tunnels with opposite starting points and heading in opposite directions are intended to meet happily in the middle: the